arXiv AI By Natan Katz

The Planar Case of Thomas Positive Circuits Conjecture

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arXiv:2607. 14143v1 Announce Type: cross Abstract: The notion of circuit refers to a cyclic oriented influence between the elements of a dynamical system.

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Equilibrium Causal Games: Separation, Identification, and the Identifiability of Cyclic Latent States

Power grids, markets, and interacting populations, settle into feedback driven equilibria observed through unknown sensors. Our Equilibrium Causal Game (ECG) joins a game to its cyclic causal model, hidden inputs, sensor map, and rules for interventions and equilibrium selection; interventions edit declared objects and recompute equilibrium.

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Real-rootedness of the Poincar\'e polynomials of $\overline{\mathcal M}_{0,n}$: an AI-assisted proof

arXiv:2605. 29151v2 Announce Type: replace-cross Abstract: We prove real-rootedness for the Poincar\'e polynomial \[ P_n(t)=\sum_{i=0}^{n-3} \dim H^{2i}(\overline{\mathcal M}_{0,n};\mathbb{Q})t^i \] of the Deligne--Mumford moduli space $\overline{\mathcal M}_{0,n}$ of stable $n$-pointed rational curves, proving a conjecture of Aluffi--Chen--Marcolli.

By Gergely B\'erczi, Young-Hoon Kiem